Guest Post by Willis Eschenbach
I’ve been listening to lots of stuff lately about tidal cycles. These exist, to be sure. However, they are fairly complex, and they only repeat (and even then only approximately) every 54 years 34 days. They also repeat (even more approximately) every 1/3 of that 54+ year cycle, which is 18 years 11 days 8 hours. This is called a “Saros cycle”. So folks talk about those cycles, and the 9 year half-Saros-cycle, and the like. The 54+ year cycle gets a lot of airtime, because people claim it is reflected in a sinusoidal approximately 54-year cycle in the for example the HadCRUT temperature records.
Now, I originally approached this tidal question from the other end. I used to run a shipyard in the Solomon Islands. The Government there was the only source of tide tables at the time, and they didn’t get around to printing them until late in the year, September or so. As a result, I had to make my own. The only thing I had for data was a printed version of the tide tables for the previous year.
What I found out then was that for any location, the tides can be calculated as a combination of “tidal constituents” of varying periods. As you might imagine, the strongest tidal constituents are half-daily, daily, monthly, and yearly. These represent the rotations of the earth, sun, and moon. There’s a list of the various tidal constituents here, none of which are longer than a year.
Figure 1. Total tidal force exerted on the Earth by the combination of the sun and the moon.
So what puzzled me even back then was, why are there no longer-period cycles used to predict the tides? Why don’t we use cycles of 18+ and 54.1 years to predict the tides?
Being a back to basics, start-from-the-start kind of guy, I reckoned that I’d just get the astronomical data, figure out the tidal force myself, and see what cycles it contains. It’s not all that complex, and the good folks at the Jet Propulsion Lab have done all the hard work with calculating the positions of the sun and moon. So off I went to JPL to get a couple hundred years data, and I calculated the tidal forces day by day. Figure 1 above shows a look at a section of my results:
These results were quite interesting to me, because they clearly show the two main influences (solar and lunar). Figure 1 also shows that the variations do not have a cycle of exactly a year—the high and low spots shift over time with respect to the years. Also, the maximum amplitude varies year to year.
For ease of calculation, I used geocentric (Earth centered) coordinates. I got the positions of the sun and moon for the same time each day from 1 January 2000 for the next 200 years, out to 1 Jan 2200. Then I calculated the tidal force for each of those days (math in the appendix). That gave me the result you see in Figure 1.
However, what I was interested in was the decomposition of the tidal force into its component cycles. In particular, I was looking for any 9 year, 18+ year, or 54.1 year cycles. So I did what you might expect. I did a Fourier analysis of the tidal cycles. Figure 2 shows those results at increasingly longer scales from top to bottom.
Figure 2. Fourier analysis of the tidal forces acting on the earth. Each succeeding graph shows a longer time period. Note the increasing scale.
The top panel shows the short-term components. These are strongest at one day, and at 29.5 days, with side peaks near the 29.5 day lunar cycle, and with weaker half-month cycles as well.
The second panel shows cycles out to 18 months. Note that the new Y-axis scale is eight times the old scale, to show the much smaller annual cycles. There are 12 month and 13.5 month cycles visible in the data, along with much smaller half-cycles (6 months and 6.75 months). You can see the difference in the scales by comparing the half-month (15 day) cycles in the top two panels.
The third panel shows cycles out to 20 years, to investigate the question of the 9 and 18+ year cycles … no joy, although there is the tiniest of cycles at about 8.75 years. Again, I’ve increased the scale, this time by 5X. You can visualize the difference by comparing the half-year (6-7 month) cycles in the second and third panels. At this scale, any 9 or 18+ year cycles would be very visible … bad news. There are no such cycles in decomposition of the data.
Finally, the fourth panel is the longest, to look for the 54 year cycle. Again, there is no such underlying sine-wave cycle.
Now, those last two panels were a surprise to me. Why are we not finding any 9, 18+, or 54 year cycle in the Fourier transform? Well … what I realized after considering this for a while is that there is not a slow sine wave fifty-four years in length in the data. Instead, the 54 years is just the length of time that goes by before a long, complex superposition of sine waves approximately repeats itself.
And the same thing is true about the 18-year Saros cycle. It’s not a gradual nine-year increase and subsequent nine-year decrease in the tidal force, as I had imagined it. Instead, it’s just the (approximate) repeat period of a complex waveform.
As a result, I fear that the common idea that the apparent ~60 year cycle in the HadCRUT temperatures is related to the 54-year tidal cycles simply isn’t true … because that 54 year repeating cycle is not a sine wave. Instead, looks like this:
Figure 3. The 54 year 34 day repetitive tidal cycle. This is the average of the 54-year 34-day cycles over the 200 years of data 2000-2200.
Now, as you can see, that is hardly the nice sine wave that folks would like to think modulates the HadCRUT4 temperatures …
This exemplifies a huge problem that I see happening. People say “OK, there’s an 18+ year Saros cycle, so I can divide that by 2. Then I’ll figure the beat frequency of that 9+ year cycle with the 8.55 year cycle of the precession of the lunar apsides, and then apply that to the temperature data …”
I’m sure that you can see the problems with that approach. You can’t take the Saros cycle, or the 54+ year cycle, and cut it in half and get a beat frequency against something else, because it’s not a sine wave, as people think.
Look, folks, with all the planets and moons up there, we can find literally hundreds and hundreds of varying length astronomical cycles. But the reality, as we see above, is not as simple as just grabbing frequencies that fit our theory, or making a beat frequency from two astronomical cycles.
So let me suggest that people who want to use astronomical cycles do what I did—plot out the real-life, actual cycle that you’re talking about. Don’t just grab the period of a couple of cycles, take the beat frequency, and call it good …
For example, if you want to claim that the combined tidal forces of Jupiter and Saturn on the sun have an effect on the climate, you can’t just grab the periods and fit the phase and amplitude to the HadCRUT data. Instead, you need to do the hard lifting, calculate the actual Jupiter-Saturn tidal forces on the sun, and see if it still makes sense.
Best regards to everyone, it’s still raining here. Last week, people were claiming that the existence of the California drought “proved” that global warming was real … this week, to hear them talk, the existence of the California floods proves the same thing.
In other words … buckle down, it’s gonna be a long fight for climate sanity, Godot’s not likely to show up for a while …
w.
THE USUAL: If you disagree with something that I or someone else said, please quote the exact words you disagree with, and tell us why. That way, we can all understand what you object to, and the exact nature of your objection.
CALCULATIONS: For ease of calculations, I downloaded the data for the sun and moon in the form of cartesian geocentric (Earth-centered) coordinates. This gave me the x, y, and z values for the moon and sun at each instant. I then calculated the distances as the square root of the sum of the squares of the xyz coordinates. The cosine of the angle between them at any instant is
(sun_x * moon_x + sun_y * moon_y + sun_z * moon_z) / (sun_distance * moon_distance)
and the combined tidal force is then
sqrt( sun_force^2 + moon_force^2 + 2* sun_force * moon_force * cos(angle))
DATA AND CODE: The original sun and moon data from JPL are here (moon) and here (sun), 20 Mb text files. The relevant data from those two files, in the form of a 13 Mb R “save()” file, is here and the R code is here.
EQUATIONS: The tidal force is equal to 2 * G * m1 * m2 * r / d^3, where G is the gravitational constant, m1 and m2 are the masses of the two objects, d is the distance between them, and r is the radius of the object where we’re calculating the tides (assuming that r is much, much smaller than d).
A good derivation of the equation for tidal force is given here.
CD:
By the way the Arctic Ocean Area is 14,056,000 km². The tidal rise/fall is only some 15mm but most of that goes in and out through the tiny gaps that are the Fram & Bering Straights. That is some multiplier. As a percentage effect against the Thermohaline flow I suspect it is non-trivial. But it is only 15mm – how COULD that possibly be important in any way?
See http://www.esr.org/AOTIM/arctic_detail.html
It is all about where you stand and what you look at.
CD:
As an example of the short term tidal flows we have that might be of interest try
http://i29.photobucket.com/albums/c274/richardlinsleyhood/ArcticOceanBarotropicTides_zps6665ba65.png
the figure out that we have NO long term variability data, Saros Cycle or not, that says how this varies with time.
Richard
Ah, I see where you are coming from now. Sorry I thought you were trying to look for “oscillations” in tidal force in a similar sense to Willis. You are looking at the effects of these tidal forcings on the atmospheric/ocean system. Then I guess you are completely right.
Ultimately, and correct me if I am wrong, you’re suggesting that to do this properly you need to discretising the Earths surface into a grid (and maybe even the atmosphere and oceans into cellular grids). Compute the tidal force at each point (rotating reference point) and then “modulate” the computed tidal forcings according to whatever local controls affect it. Then you’re in a state to examine/predict how the tidal force affects the climate. At even modest resolutions this would require a lot of CPU, physical storage and memory to do…phew!
That sounds like the way to go but it is a big ask for a blogger.
C.
cd says:
February 14, 2014 at 6:46 am
“That sounds like the way to go but it is a big ask for a blogger.”
Doing it just for the gravity field deltas alone in 3D/time is fairly non trivial. Doing it with the geography and fluidics becomes significantly greater.
Hence the request for s super-computer and the belief that a simply JPL plot does not do the problem justice.
It dismisses it almost to the point of deliberate ignorance.
CD:
Willis came into this post, at least in part I believe, to dismiss my observations that there is some sort of nearly regular pattern to the temperature data.
http://i29.photobucket.com/albums/c274/richardlinsleyhood/Fig8HadCrutGISSRSSandUAHGlobalAnnualAnomalies-Aligned1979-2013withGaussianlowpassandSavitzky-Golay15yearfilters_zps670ad950.png
I have in fact posed that this variation might, just might, be Lunar/Solar gravity field related with some form of Saros cycle sub-component to it.
The JPL plot was his, fairly crude, attempt to put a stake through its heart so all could rest assured that there was nothing there to frighten the children.
In fact all it has done is provide support from Tallbloke of a temperature variation in the literature that has previously linked North Atlantic sea temperature to a Lunar cycle.
http://i29.photobucket.com/albums/c274/richardlinsleyhood/200YearsofTemperatureSatelliteThermometerandProxy_zps0436b1f2.gif
Still looking for some funding and a super-computer to allow further investigations 🙂
Richard
I can see what you’re doing. Unfortunately you have such a short data set.
Have used the residual temperatures after fitting say a 2nd order polynomial. It might be easier to see correspondence when you plot both data sets together when the trend has been removed.
How does your data set map with shifts in PDO polarity.
As for super computers you can rent processing time on remote systems via Amazon (it’s not too expensive). If you can parallel code your stuff then you’ll effectively have a super computer.
cd says:
February 14, 2014 at 7:43 am
“I can see what you’re doing. Unfortunately you have such a short data set.”
The perennial cry of anyone doing serious examination of the data available. Still – work with what we have.
“Have used the residual temperatures after fitting say a 2nd order polynomial. It might be easier to see correspondence when you plot both data sets together when the trend has been removed.”
Now you ask the two things I most hate.
Curve fitting and trend removal.
I stick with full kernel filtering of the data to be absolutely certain that I am making no assumptions.
I only added the S-G on because Nate Drak PhD decided to put me down by using it (see the Nature Missing Heat thread for how that all came about). Nasty – hissy – spity argumentative style so I credit him with his PhD he was unwise enough to put it on the table during that bun fight).
I hate estimation. You make an assumption that then determines what you see. You can never be sure after that if what your seeing is what’s there or it is what your assumptions says is there.
Trend removal is likewise. The methodology you use to remove a trend just makes too much pre-decision about what you’ll find later.
I have the same (or similar) figures everywhere I run a 15 year corner low pass on the data sets. AMO, PDO, HadCrut, GISS, even UAH and RSS if you allow the shortness of the data set to not be an obstacle (needs some kernel widening so I remain cautious on that as a definitive conclusion).
I am currently wading through proxy data sets to add them to the mix. The ~60 year picture is ‘sort of’ visible in those as well. So many proxy sets, so much work to do.
Now ~60 years could be anywhere from 55 to 75 and I wouldn’t worry. 2 cycle counts is just too short to call it even to that level of accuracy. And that would assume only one component to look for.
Yndestad’s et al work seems to be interesting. A nice long sea temp data set to work with. Another paper or two to go on the pile.
Computers are not really the problem. I use that as a foil. Drawing together all the data sets into a single format is the larger challenge to make a real 200+ year comparator. That is turning out to be a useful tool to compare suggestions to. Slightly longer than the data sets used for most people to get to a conclusion they draw. Allows for seeing how those claims fit against just a slightly longer baseline. Small enough backwards in time to have less error propagation in them as well. If proxies fit an overlap period to 1850 then 1800 should be no great push.
Then and only then might it be possible to do the 3D/time gravity plots and start doing a meaningful comparison.
“The addition of noise and low cycle counts in the sample period in question makes FFTs fairly useless as a tool for longer wavelength analysis IMHO. I am sure you will disagree but I do have to make my point.”
Not at all, I agree with the gist of it. “Useless” is overstating the problem but that’s were understanding and experience comes in. No just pressing the FFT button in your software.
Since the dataset is a time window on the real events and often we need to further distort with a window function (or “taper”) the longer periods coming out are very uncertain. That’s one of the reasons why I usually work with dT/dt when doing FFT on climate, and also to remove the autoregressive nature of the data.
On the typically 150y kind of data we have I tend to concentrate on <22y as useful range , there's frequently notable energy around 34 but it shifts a lot due to this problem.
If you try FFT on data with an upward trend you're going to get a lot of spurious bumps. FFT requires "stationary" data , ie no upward trend in the mean and no cycles close to the window length. Window fns help with the latter but you need to be careful.
Once you get around 10y periods you are on much firmer ground.
This is one of the few areas where I think the data if fairly immune to the blatant manipulation, it would be far to complicated to fabricate and trick it do fit the agenda anyone may want to insert to "save the planet".
I have however, found that hadSST messes with 9 year peaks. Probably a result of the iterative running means, "anomaly" reference periods and monthly sub-sampling without anti-alias….. it's a mess.
Despite it's obvious bumps and warts, I stick to ICOADS which is nearer to real data.
If I saw a 60 year peak in FFT from 150 y dataset I'd probably conclude it was between 50 and 70 and would expect to be change dramatically depending on which window fn I chose.
Greg Goodman says:
February 14, 2014 at 8:57 am
“Not at all, I agree with the gist of it. “Useless” is overstating the problem but that’s were understanding and experience comes in. No just pressing the FFT button in your software.”
Yes I know – I try to stay within my areas of confidence and not stray too far out of my comfort zone.
“If I saw a 60 year peak in FFT from 150 y dataset I’d probably conclude it was between 50 and 70 and would expect to be change dramatically depending on which window fn I chose.”
Given the cycle counts involved and, as far as I can see this is not even symmetrical, longer ‘positive’ than ‘negative’ at present, I would agree.
The problem I have is that it is precisely this area that my 15 corner CTRM (my terminology for your 3RM you used) shows that there is something there.
Below 15 years there are a lot of potential cycles from 4 years or so and all the way up to 15. That definitely in FFT territory which I suspect you will be much better experienced to determine than I.
Edit: shorter‘positive’ than ‘negative’ (Approx 55-60 years top, 65-70 year bottom).
I’ve been digging out some more accurate numbers for the astronomical values (hard to find accurate and consistent values once you ask for 5 sig.fig).
As Willis astutely noticed there was a small discrepancy between the harmonic result of adding 18.03 and 8.85 . I did not pay too much notice because of the accuracy of the starting numbers did not seem to warrant it and Jupiter, while being the king of the planetary gods, is not alone in the skies.
I didn’t follow how Willis got his 500 years or whatever value, but astronomic cycles are pretty steady and so it’s fair to look at how long it would take to the two cycles to drift out of phase. Willis seems stuck on “beats”
http://en.wikipedia.org/wiki/Beat_%28acoustics%29
The beat period is the time it takes the cycles to go from being in phase to being in anti-phase, ie half the full cycle.
The following figures should be accurate to at least 6 sf. I haven’t cropped them until the end to avoid introducing further rounding errors.
pSaros= 18.0310284658705
pApsides=8.85259137577002
days_per_year = 365.25636
print 2/(1/pApsides+1/pSaros)
pApSaros=11.8749876715626
As I noted that is very, very close to Jupiter’s sideral orbital period. (fixed stars).
pJ= 4332.589 / days_per_year # = 11.861775658061
Now looking as W. did at how long these cycles take to drift in phase and come back into phase:
print 2/(1/pJ-1/pApSaros) = 21322 years
http://en.wikipedia.org/wiki/Apsidal_precession
“These two forms of ‘precession’ combine so that it takes over 21,600 years for the ellipse to revolve once relative to the vernal equinox” [Note this is the Earth’s apsides (perihelion/aphelion) now, not the the lunar perigee cycle. ]
Now that Jupiter causes some of the irregularities in the lunar orbit is not contentious. So the initial result did not surprise me that much . It seems too close to be pure coincidence.
For the second number, it will be very sensitive to errors in original data because it is the reciprocal of a very small difference term. So some care is needed.
What I find most surprising about this is that it seems to imply that the link between the luni-solar “saros” period and the lunar apsides only depends on Jupiter whereas I would expect a very minor influence from the other planets too.
Now I’m sure someone is going to start wailing about numerology because I have not suggested a direct physical mechanism. But since no one on earth can solve a three body problem and this involves four bodies, that is rather an unrealistic demand.
The best we can do is observe and analyse to see if we can increase our understanding.
Now even if this is one huge coincidence , a cruel trick played on us by the white mice to study how humans react when they throw shit like this at us, it could explain where “jupiter-like” frequencies come from if they are found.
In fact, I’d be pretty surprised that someone who is will up on astronomy doesn’t point out this was noticed long ago. Richard said he’d heard of a resonance but could not remember where.
Greg:
I am certain that until someone (me?) gets round to doing a full global 3d vector/time map of how the Moon/Sun Saros cycle field plays out here on the Earth’s surface none of us knows if this will prove to be interesting or just a goose chase.
The main problem is not really with the surface tide, even if is amplified to some extend by sloping sea floors, but the Internal tide. This is where it gets really interesting as it is this sub-surface tidal interface that has the most chance of augmenting/preventing North/South water exchange. And it has a significantly larger tidal range than the surface one does. 10’s of meters, not the 0.3 meters or so. Difference between air/water and water/water intefaces.
The volumes, temperature differences and the relatively small vertical sections through which all this happens are ripe for casual interactions that may well not show at first glance.
And there may be nothing there anyway!
But everywhere I look there are things that say something natural is happen at these timescales and with a significant peak to peak range. Something like 20-30% of the total range seen so far in the high quality data.
You just can’t overlook that! Well I can’t anyway.
What’s this vector map you want to see?
Willis has extracted ephemeris data for both sun and moon position in xyz . Though he did not calculate the resultant vector explicitly , that’s trivial.
I think the along axis vector is a reasonable estimation of the combined force , at least from the point of view of looking at variations in amplitude over time. It’s probably not too far off as an estimation of magnitude either. Obviously, even if you sum all points across the earth the resultant vector will be along E-M axis.
neither would it be too hard to do an 2D integral across theta,phi if you really wanted to. Just do a bit of trigonometry to get and expression for the force at one point in terms of the angles.
Adding a few lines to Willis code should produce a graph of what you want.
Greg:
A few moments of Google and thinking means that it all would be a pointless exercise anyway, but thanks for the offer. I started out with a ‘well someone must have done this before so…” and soon came to realise why this would have all been futile.
Just the principal lunar semi-diurnal also known as the M2 (or M2) tidal constituent (from Wiki) looks like this when actually you do the ‘how does the Earth actually respond to the tidal vector field’ question.
http://i29.photobucket.com/albums/c274/richardlinsleyhood/M2_tidal_constituent_zps8ce22394.png
Now with the best will in the world no JPL plot is going to get to that!
And this (with a ~60 year time component added to get the series) is what is really needed! A movie of how that changes.
And look where one of the big red patches is, just below the important Greenland – Scotland ridge.
Not affect Climate indeed. Head post dismissed with one image.
Greg: Add to that I love to see this as a 4 * 18.6 year movie as well
http://i29.photobucket.com/albums/c274/richardlinsleyhood/ArcticOceanBarotropicTides_zps6665ba65.png
Oh yeah, the naive idea of tidal bulges is bullshit in terms of what really happens.
Oh the first graph you linked you can see the amphidromes I mentioned recently . The tides actually rotate about these points that have near ZERO tidal amplitude 24/7.
The first amphidrome to be discovered was the one about half between California and Hawaii IIRC.
Greg:
I just spent way to much time trying to get Willis to see that his view of the world was so narrowly focused that it had no real meaning and did not stop to think of how to put my overall point of view into a single image.
I think both of those two images (expressed as 4 * 18.6 year movies) pretty well sums up what could be of interest to Climate and why it has never been done yet.
To prove (or disprove) what I see as a possibility – just a possibility at this point in time – will take a little more than an overly simplified JPL plot.
Still it has given me the chance to refine what I say and how I say it so not everything was a waste of time.
Bye the bye, do you mind if I (re)use those two frequency plots from the Running Means thread in some work I am doing? I’ve stuck a copyright and ref url on the image so there is no doubt as to origin and copyright.
cd says:
February 13, 2014 at 11:32 pm
cd, first, thanks for your measured response and tone, much appreciated.
Next, you and Richard both seem to think I’m talking about a 1-D vector. As near as I can tell, what you mean by that is a signed number, with the sign (+ or -) giving the direction, and the magnitude being the value of the number.
But if you will notice, the magnitude of the tidal force is never negative. In fact, magnitudes by definition are always positive. Let me give you a real world example.
Speed is the magnitude of the velocity vector. And since it is a magnitude, there’s no such thing as going minus 60 miles per hour. Because speed is a magnitude, it is always positive. You can’t go minus sixty miles an hour. You can only go sixty miles an hour in a variety of directions. Backing up doesn’t mean you’ve stopped traveling, you are still making mileage, just in a different direction.
Now, if I’m discussing speed, would you make the claim that the speed is a 1D vector? No … because it’s not a 1-D vector. It’s not a vector at all. It is the instantaneous magnitude of a 3D vector. According to you, a 1D vector could have the value of -60 … but the speed can’t have that value.
So that was the first problem.
The second problem was that Richard, as is his wont, was just trying to be obstructive. He is making a point which in addition to being incorrect is meaningless. What does the question of 1D vs 3D have to do with the ebb and flow of the strength of the tidal force? He was just trying to derail the discussion, and then you had to jump in … at which point I over-reacted, and instead of politely asking you to butt out and let Richard explain his own words, I snapped back at you. Ah, well, live and learn, mea maxima culpa.
You go on to say:
cd says:
February 13, 2014 at 12:30 pm
Was there some part of me saying QUOTE MY WORDS that escaped you, or did you read it and deliberately ignore it? Or is it your normal practice to just fling mud randomly and hope that some of it sticks?
I’m honest about what I’m doing here and in my life, cd—learning things. When I learn them, I apply them in what I see as new and ingenious ways to a variety of old puzzles … don’t you?
If you have evidence that I ran aground in that process of applying newly-learned methods to a variety of problems, which you and I both do, then please, bring it on. I’m more than happy to defend what I’ve written.
In future, however, please refrain from making unsupported, uncited allegations of wrongdoing … not polite at all.
w.
PS—You accuse me of “having form” in this, a lovely British term meaning to have a history of doing something.
On the other hand, to use your terms, you have “no form” in this at all. Why not?
Because you are anonymous. Last week you could have been “ab”, and next week you could easily be “ef”. You don’t have the courage to stand behind your own words—you can disown them more easily than changing a shirt.
Since you are a man without the courage to sign his own words and thus to have an actual history like an honest man has, for you to accuse me of “having form” is cowardly. Come back a few years after you’ve built up the nerve to sign your opinions, when you have a history, and you’ll have a place to stand on while dissecting my history … until then, you’re just another random anonymous internet popup, and I weight your words accordingly.
Willis Eschenbach says:
February 14, 2014 at 1:00 pm
“Next, you and Richard both seem to think I’m talking about a 1-D vector. As near as I can tell, what you mean by that is a signed number, with the sign (+ or -) giving the direction, and the magnitude being the value of the number.”
Think of it being like a piece of string (a vector/line/or whatever else you wish) pointing along the balance point (in vector space) between the lines linking the centre of the Earth to Moon and Sun.
That whirling, changing line is what you have then plotted the height of the force on. The magnitude of the vector sum your transpositions have given you.
Of course that whirling piece of string cuts through the Earth’s surface in a complex spiralling path that takes no note of the land/ocean it crosses.
And that is the first of the problems. It is not oriented to the places on the surface it crosses. Nothing wrong mathematically in that, but not much use as it stands.
Climate is solidly attached to the surface (well relative movements to it anyway) so you need to look at things from that point of view to get whatever effects and interactions could occur.
But this is all a distraction really (and I am not trying to be antagonistic here) the problem is that if (and it is very much still IF) this does eventually have some effect on climate then this
http://i29.photobucket.com/albums/c274/richardlinsleyhood/M2_tidal_constituent_zps8ce22394.png
is what the Climate will be looking at. A movie over 4 * 18.6 years worth of how that pattern changes.
And I hope you will agree that this is a much more complex (and in a way much more interesting) question to consider.
“Bye the bye, do you mind if I (re)use those two frequency plots from the Running Means thread in some work I am doing? I’ve stuck a copyright and ref url on the image so there is no doubt as to origin and copyright.”
No problem in principal , in fact I think you’ll find that as soon as you publish an image on wordpress.com it becomes CreativeCommons copyright.
which ones did you mean?
Willis Eschenbach says:
February 14, 2014 at 1:00 pm
“The second problem was that Richard, as is his wont, was just trying to be obstructive.”
Now you do me a disservice. I am never obstructive, stubborn maybe, never obstructive.
I realise all too well that it is my fault I am unable to covey the point (line/vector/whatever) that I see. I try hard to change the words, adopt another point of view, express it as best I can in words that will carry meaning to you. I am still failing but, with your perseverance, I will continue trying.
No malice,. No anger. No rude words. Occasionally testy but I do try to apologize if that occurs. No-one is perfect.
So have I explained it well enough yet? Is there some other way I can give you the place I stand on so that you too can see the picture I see. I do hope so.
This is a detailed, wonderful picture with no easy explanations or remedies. Some really sloppy maths (not by you – down boy) that are in common use. Sub-sampled Single Means – who could ever get a paper published using those? Seems common place in Climate. So demonstrably wrong in hurts. Producing errors that are then baked into the and given as though they were gospel (and with a religious fervour too boot).
Some really sloppy assumptions (again not by you) where ‘it looks like it might fit – that must be the reason’ is advanced all the time. No backing. No curiosity after the choice is made. Full steam and damn the Icebergs.
Greg Goodman says:
February 14, 2014 at 1:44 pm
“No problem in principal”
Thanks.
“which ones did you mean?”
http://i29.photobucket.com/albums/c274/richardlinsleyhood/Fig1GaussianSimpleMeanFrequencyPlots_zpsbea1daf4.png
http://i29.photobucket.com/albums/c274/richardlinsleyhood/Fig2LowPassGaussianCTRMcompare_zps4d63c75e.png
I’ve taken a closer look at Indian ocean SST since it shows clear 9.3 years rather that the composite 9.07 found in Pacific and Atlantic SST. This is probably because it is land bound on the northern side.
http://climategrog.wordpress.com/?attachment_id=777
Having split it into Tropical (15S-15N) and extra-tropical (55S-15S) I found a NEGATIVELY correlation peak at 9.31 years. That means one zone cools while the other warms.
9.31 is half the lunar nodal precession that determines the declination angle.
Since the either the front or back aspect of the tide raising force will be in each hemisphere it only the magnitude of the declination angle which is relevant. Hence half the circa 18.6 year period.
This would seem to be clear evidence of warm water being drawn away from the tropics when declination is more pronounced.
Greg: So why would we get a doubling of the frequency as such? I can see why one peak, Why the other?
I just posted what I believe explains the origin of tides on planets with orbital moons and/or in orbit themselves around the sun.
http://clivebest.com/blog/?p=5572
Tides must also play a role in the earth’s climate.
The tide raising force acts in both directions ( bulge on each side in the simplistic model).
Zero declination, with sun and moon over equator is neutral, a deviation either N or S will cause a “bulge” on in both hemispheres or roughly equal proportions. It should be like a rectified sine wave in both hemispheres and in phase. Though inertia of the water mass will round off the pointy bit where it changes over. FFT is just picking up the principal frequency, maybe more digging would find the higher harmonics which would be present in the spectrum of full-wave rectified signal.